Spurious Reflections Research Articles

Ind_X: program for indexing single-crystal diffraction patterns

Indexing is an essential step in analysis of diffraction patterns. Diffraction of monochromatic radiation by a single crystal provides approximate positions of some nodes of the reciprocal lattice of the crystal, and the indexing problem lies in determining a lattice matching these positions.Ind_X is a program for indexing diffraction data given in the form of several approximate reciprocal lattice nodes. The applied method relies on testing potential volumes of the primitive cell of the reciprocal lattice. A subset of reciprocal lattice vectors supporting a given test volume is used to obtain tentative lattice bases. These are bases of low-index superlattices of lattices based on triplets of supporting vectors. TheInd_X solution of the indexing problem consists of a list of best bases. The method turns out to be quite robust to data inaccuracies and spurious reflections. The program is relatively versatile, easily operated and freely accessible.

Dynamic 2.5-D Green's function for a point load or a point fluid source in a layered poroelastic half-space

The complete dynamic two-and-a-half-dimensional (2.5-D) Green's function for an internal point load or fluid source buried in a layered poroelastic half-space is derived and applied to the 2.5-D boundary element method (BEM) in this paper. Based on Biot's theory, the general solutions are derived using the potential decomposition method and the Fourier transform. Utilizing the boundary conditions of the free surface, interfaces and bottom half-space, as well as the general solutions, the complete 2.5-D Green's function for a layered poroelastic half-space is obtained using the transmission and reflection matrix (TRM) method. The solutions presented in this paper are free of numerical instability for the high frequency and large layer thickness. The proposed 2.5-D Green's function is verified by comparison with the existing solutions. A case study of calculating vibrations from a semi-circular tunnel embedded in a layered poroelastic half-space is presented using the 2.5-D BEM along with the proposed 2.5-D Green's function. The layer interfaces and the surface of the poroelastic half-space no longer have to be meshed, avoiding spurious reflections at mesh truncations. The boundary element mesh can be limited to the surface of the tunnel, significantly reducing the size of the boundary element mesh.

Dual-horizon peridynamics: A stable solution to varying horizons

In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.

Dielectric Resonator Metasurface for Dispersion Engineering

We introduce a practical dielectric metasurface design for microwave frequencies. The metasurface is made of an array of dielectric resonators held together by dielectric connections thus avoiding the need of a mechanical support in the form of a dielectric slab and the spurious multiple reflections that such a slab would generate. The proposed design can be used either for broadband metasurface applications or monochromatic wave transformations. The capabilities of the concept to manipulate the transmission phase and amplitude of the metasurface are supported by numerical and experimental results. Finally, a half-wave plate and a quarter-wave plate have been realized with the proposed concept.

IMPLEMENTATION OF A NON-SPLITTING FORMULATION OF PERFECTLY MATCHED LAYER IN A 3D – 4TH ORDER STAGGERED-GRID VELOCITY-STRESS FINITE-DIFFERENCE SCHEME

One of the major problems in numerical simulations of wave propagation in elastodynamics using grid-point methods is the truncation of the computational space by artificial boundaries. These boundaries produce spurious reflections, polluting the results with artificial noise, therefore several efforts have been realized in order to achieve transparent or non-reflecting boundaries for truncating the computational space. Perfectly Matched Layer (PML) has been one of the most efficient methods for implementing artificial boundaries at the edges of the computational models. However the application of PML requires the “tuning” of several variables, for which very limited work has been presented. In the present study we employ the Non-Splitting formulation of PML (NPML) technique presented by Wang & Tang (2003), based on the introduction of small perturbations in the wavefield. The NPML formulation shows the same accuracy with the originally introduced PML but is easier to be implemented because it does not require the field splitting. The main scope of this paper is to perform a full analysis of the efficiency of NMPL based on numerical tests using a 3D–4th order staggered-grid velocity-stress finite-difference scheme. The analysis consists of direct, quantified comparisons with reference solution waveforms from a semi-analytical method (Discrete Wavenumber Method) with synthetic waveforms produced using the most popular Absorbing Boundary Conditions (ABCs) and PML, in various canonical models (homogeneous and layer over half-space).

DEM–FEM analysis of soil failure process via the separate edge coupling method

SummaryThe concurrent multiscale method, which couples the discrete element method (DEM) for predicting the local micro‐scale evolution of the soil particle skeleton with the finite element method (FEM) for estimating the remaining macro‐scale continuum deformation, is a versatile tool for modeling the failure process of soil masses. This paper presents the separate edge coupling method, which is degenerated from the generalized bridging domain method and is good at eliminating spurious reflections that are induced by coupling models of different scales, to capture the granular behavior in the domain of interest and to coarsen the mesh to save computational cost in the remaining domain. Cundall non‐viscous damping was used as numerical damping to dissipate the kinetic energy for simulating static failure problems. The proposed coupled DEM–FEM scheme was adopted to model the wave propagation in a 1D steel bar, a soil slope because of the effect of a shallow foundation and a plane‐strain cone penetration test (CPT). The numerical results show that the separate edge coupling method is effective when it is adopted for a problem with Cundall non‐viscous damping; it qualitatively reproduces the failure process of the soil masses and is consistent with the full micro‐scale discrete element model. Stress discontinuity is found in the coupling domain. Copyright © 2017 John Wiley & Sons, Ltd.

Perfectly matched layer for an elastic parabolic equation model in ocean acoustics

The perfectly matched layer (PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation (PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide (Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Pade approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer (ABL) both in acoustic and seismo-acoustic sound propagation modeling.

A novel CFS‐PML boundary condition for transient electromagnetic simulation using a fictitious wave domain method

AbstractIn this study, we apply fictitious wave domain (FWD) methods, based on the correspondence principle for the wave and diffusion fields, to finite difference (FD) modeling of transient electromagnetic (TEM) diffusion problems for geophysical applications. A novel complex frequency shifted perfectly matched layer (PML) boundary condition is adapted to the FWD to truncate the computational domain, with the maximum electromagnetic wave propagation velocity in the FWD used to set the absorbing parameters for the boundary layers. Using domains of varying spatial extent we demonstrate that these boundary conditions offer significant improvements over simpler PML approaches, which can result in spurious reflections and large errors in the FWD solutions, especially for low frequencies and late times. In our development, resistive air layers are directly included in the FWD, allowing simulation of TEM responses in the presence of topography, as is commonly encountered in geophysical applications. We compare responses obtained by our new FD‐FWD approach and with the spectral Lanczos decomposition method on 3‐D resistivity models of varying complexity. The comparisons demonstrate that our absorbing boundary condition in FWD for the TEM diffusion problems works well even in complex high‐contrast conductivity models.

High Precision Laser Scanning of Metallic Surfaces

Speckle noise, dynamic range of light intensity, and spurious reflections are major challenges when laser scanners are used for 3D surface acquisition. In this work, a series of image processing operations, that is, Spatial Compound Imaging, High Dynamic Range Extension, Gray Level Transformation, and Most Similar Nearest Neighbor are proposed to overcome the challenges coming from the target surface. A prototype scanner for metallic surfaces is designed to explore combinations of these image processing operations. The main goal is to find the combination of operations that will lead to the highest possible robustness and measurement precision at the lowest possible computational load. Inspection of metallic tools where the surface of its edge must be measured at micrometer precision is our test case. Precision of heights measured without using the proposed image processing is firstly analyzed to be ±7.6 μm at 68% confidence level. The best achieved height precision was ±4.2 μm. This improvement comes at 24 times longer processing time and five times longer scanning time. Dynamic range extension of the image capture improves robustness since the numbers of saturated or underexposed pixels are substantially reduced. Using a high dynamic range (HDR) camera offers a compromise between processing time, robustness, and precision.

Complex-Frequency Shifted PMLs for Maxwell’s Equations With Hyperbolic Divergence Cleaning and Their Application in Particle-in-Cell Codes

The simulation of unbounded domains inevitably requires an artificial truncation of the computational domain and spurious reflections resulting from this procedure are a common problem. In this paper, a perfectly matched layer formulation for Maxwell’s equations in purely hyperbolic form is presented. The model is applied to standard wave attenuation problems and particle-in-cell simulations of electron beam devices.

Non-reflecting coupling method for one-dimensional finite difference/finite volume schemes based on spectral error analysis

Abstract For the compressible coupled simulation of piping systems including fluid machinery, an embedment of 3D finite volume schemes for active components such as pumps and compressors into 1D finite difference characteristic methods for passive components (e.g. pipes, valves) offers a sophisticated 3D investigation of the machinery with a moderate simulation effort for the entire system. While a 3D-1D coupling method for finite volume Godunov schemes is available from preliminary studies, in the present paper, a new non-reflecting coupling method for 1D finite volume Godunov and 1D finite difference characteristic methods is presented, and the mechanisms for spurious reflections at the coupling interface are revealed. The proposed methodology is based on spectral error analysis and is in general applicable to the coupling of any fundamentally different numerical schemes. It is demonstrated that by matching the numerical diffusion and speed of sound in both coupled domains, reflections can be minimized.

Wave filtering through a selective perfectly matched layer in multiscale couplings with dynamically incompatible models

SummaryIn this paper, we develop a strategy that enables a consistent wave transfer when coupling mechanical models exhibiting various description scales under dynamic loading. Incompatibilities between concurrent models are addressed by a selective filtering based on the perfectly matched layer framework and involving a dedicated projection operator. This filtering, performed in the vicinity of the coupling interface, aims at avoiding spurious wave reflections by automatically killing part of the signal with wavelength range not compatible with the downstream (coarser scale) model while the relevant complementary part is transferred. Performances of the proposed approach are evaluated in details by conducting one‐dimensional and two‐dimensional numerical experiments. The definition of the projection operator, which is a key point of the method, is particularly tackled by analyzing and comparing several possible choices. Copyright © 2016 John Wiley & Sons, Ltd.

Cost effective wavelength reused MDM system for bidirectional mobile fronthaul.

In this paper, we propose a cost-effective wavelength-reused mode-division-multiplexing (MDM) system for high speed symmetrical bidirectional mobile fronthaul application. At the base band unit (BBU) pool, one of the spatial modes is used to transmit signal carrier while the others are used for downstream (DS) signal channels. At the remote radio unit (RRU) side, the signal carrier is split and reused as modulation carrier for all the upstream (US) signal channels after mode demultiplexing. Thanks to the low mode crosstalk characteristic of the mode multiplexer/demultiplexer (MUX/DEMUX) and few-mode fiber (FMF), the signal carrier and each signal channel can be effectively separated. The spectral efficiency (SE) is significantly enhanced when multiple spatial channels are used. Compared with other wavelength reused scheme in which the downstream and upstream be modulated in orthogonal dimension, the modulation format of both directions are independent in the proposed wavelength reused MDM system. Therefore, it can easily achieve symmetrical bidirectional transmission without residual re-modulation crosstalk. The proposed scheme is scalable to multi-wavelength application when wavelength MUX/DEMUX is utilized. With the proposed scheme, we demonstrate a proof of concept intensity modulated 4 × 25-Gb/s 16-QAM orthogonal frequency division multiplexing (OFDM) transmission over 10-km FMF using low modal-crosstalk two-mode FMF and MUX/DEMUX with error free operation. The downstream receiver sensitivity is -21 dBm while the upstream receiver sensitivity is -18 dBm for bidirectional transmission. Due to the Rayleigh backscattering and other spurious reflections, the upstream suffers 2 dB power penalty compared with unidirectional transmission without downstream. To mitigate bidirectional transmission impairments, we propose a simple and effective method to suppress Rayleigh backscattering by shifting the downstream subcarrier frequency. A receiver sensitivity improvement of up to 2.5 dB is achieved for upstream with different downstream power.

The effect of boundary conditions, model size and damping models in the finite element modelling of a moving load on a track/ground system

An investigation is presented of the use of finite element models in the time domain to represent a load moving on a railway track on a flexible ground. A systematic study is carried out to compare different sizes and shapes of finite element mesh, different boundary conditions intended for suppressing reflections from the truncated model boundaries, and different models of soil damping. The purpose is to develop guidance to assist in selecting appropriate finite element models for moving load problems. To prevent reflections from the boundaries of the finite domain two approaches are compared. A 40m radius hemispherical finite element mesh has been used first with infinite elements around the perimeter. This approach gives good results for a point harmonic load at the centre of the domain but some problems are highlighted when it is used for moving load calculations. An alternative approach has therefore been investigated based on a cuboid mesh. The base was fixed to prevent rigid-body motions of the model and, rather than use infinite elements at the sides, these were also fixed. It is shown that, provided that a suitable damping model is used, the spurious reflections from the sides of the model can be suppressed if the model is wide enough. On the other hand, if infinite elements are used, the calculations are found to be considerably more costly with little added benefit. Different models of soil damping are also compared. It is shown that a mass-proportional damping model gives a decay with distance that is independent of frequency, making it particularly suitable for this application. The length of model required to achieve steady state has been investigated. For a homogeneous half-space it is found that the required length increases considerably in the vicinity of the critical speed, up to 130m in the present example, whereas for the layered ground a more modest length is sufficient for all speeds.

Open boundary conditions for tidally and subtidally forced circulation in a limited‐area coastal model using the Regional Ocean Modeling System (ROMS)

AbstractIn limited‐area ocean models, open boundary conditions (OBCs) often create dynamic inconsistencies and perform poorly in resolving tidal or subtidal flow when both forces exist. Orlanski‐type radiation OBCs are reasonably efficient at treating the subtidally forced flow, and Flather‐type OBCs are commonly adapted for the tidally forced flow. However, neither of them performs well when tidal and subtidal forces simultaneously drive the flows. We have developed a novel OBC that integrates the active OBC in Gan and Allen (2005) and a Flather‐type OBC. This new OBC accommodates the concurrent Tidal and Subtidal (TST) forcing, and the respective tidal or subtidal forcing, at the open boundary of a limited‐area model. This new TST‐OBC treats the tidal component with a Flather‐type OBC, and it separates subtidal barotropic and baroclinic components into local (forced) and global (unforced) components. Then an unforced Orlanski‐type OBC can be applied to the global part. We applied the TST‐OBC to all model variables to reduce dynamic inconsistence. Using the Regional Ocean Modeling System, we applied the TST‐OBC to the shallow East China Sea shelf where strong tidal and subtidal forces over complex topography govern the circulation. Our numerical experiments and analyses suggest that the TST‐OBC was robust for both concurrent tidal‐subtidal forcing and solely tidal or subtidal forcing at the open boundary. It reduced spurious energy reflection, and, overall, it performed better than an Orlanski‐type or Flather‐type OBC in reproducing realistic tidal and subtidal shelf circulation.

TOWARD MULTISCALE MODELING OF WAVE PROPAGATION IN ARTERIES

In this study, we apply a novel numerical technique for modeling the propagation of mechanical wave in the human arteries using the multiscale method. We define a particle region characterized by molecular dynamics (MD) method which is surrounded by a continuous region characterized by a finite element (FE) method. The interface between the two models are defined so as to minimize spurious reflections at the interface. This is a preliminary work for the modeling of the mechanical stability of atherosclerosis plaques using multiscale method. The model offered has extensive application in cell mechanics.

Three-dimensional detonation simulations with the mapped WENO-Z finite difference scheme

Abstract We perform a very long time numerical simulation to capture the three-dimensional detonation structures in a rectangular duct by solving the reactive Euler equations using the high order/resolution WENO-Z conservative finite difference scheme (Gao et al. J. Sci. Comput. 55 : 351–371, 2013). In the algorithm, the perfectly matched layer (PML) absorbing boundary condition (ABC) for the reactive Euler equations is used to reduce the spurious wave reflection from the open left boundary which allows one to use a significant smaller truncated physical domain. Moreover, a tangent grid mapping is used to enhance the grid resolution within the half reaction zone that greatly reduces the memory usage and computational time compared with solving the problem with a uniform grid. The initial Zeldovich-von Neumann-Doring (ZND) profile of two classical stable and slightly unstable detonation waves is perturbed to generate the rectangular in-phase, diagonal in-phase and spinning detonation structures. Depending on the initial perturbation, the stable case shows the presence of a rectangular mode and a diagonal mode of the detonation front, which are suggested to be geometrically similar. The slightly unstable case, as expected, generates the spinning detonations instead in a narrow duct. The results show that a short time simulation is insufficient to capture the cellular detonation structures. The width-to-length ratio of the cellular patterns depends on the gas properties only, but independent of the perturbation of the initial conditions.

A perfectly matched layer formulation for modeling transient wave propagation in an unbounded fluid-solid medium.

Wave propagation in an infinite medium can be numerically simulated by surrounding a finite region by a perfectly matched layer (PML). When the medium is heterogeneous consisting of both solids and liquids, careful consideration is needed in specifying the properties of the PML especially because parts of it lie at the solid-fluid interface. While such a situation could arise in many important fields including marine seismology, where water is in contact with earth, and in biomedical ultrasound, where soft tissue is in contact with bone, no PML formulation exists to appropriately model such coupled problems. Here, a second-order time-domain PML formulation for fluid-solid heterogeneous media in two dimensions that satisfies the interface coupling boundary condition throughout the computational domain is presented. Numerical results are given to establish the applicability and accuracy of such a PML formulation in discrete settings without causing stability issues, spurious reflections, or any other problems. In particular, the effectiveness of the PML in absorbing all kinds of bulk waves, as well as surface and evanescent waves, is studied.

ALmost EXact boundary conditions for transient Schrödinger–Poisson system

For the Schrodinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. 1, yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

A New Approach of Rotated Staggered Grid FD Method With Unsplit Convolutional PML for GPR

We introduce a novel implementation of a rotated staggered grid (RSG) finite difference (FD) method based on the unsplit convolutional perfectly matched layer (UCPML). The method is carried out using rotated staggered FD operators and a general complex frequency shifted stretching factor. It can offer a number of advantages over the RSG with split convolutional perfectly matched layer (SCPML), such as improving computational efficiency, overcoming the numerical dispersions resulting from the high-frequency propagation and strong contrasts in material, and specifically absorbing the evanescent modes at grazing incidence. A half-space numerical example with a lossy medium attached demonstrates that large-scale spurious reflections and evanescent modes at grazing incidence are absorbed efficiently by the UCPML in RSG scheme. Meanwhile, the comparison of the reflection error between the proposed algorithm and traditional approaches [using time-dependent reflection error (TDRE) and frequency-dependent reflection error (FDRE)] suggests that the proposed algorithm of RSG provides a preferable improvement in absorbing low-frequency coda wave of evanescent modes, particularly in the lossy medium that possesses inhomogeneous discontinuities.